Modular multilevel converters (MMCs) play an important role in the power electronics industry due to their many advantages, such as modularity and reliability. In the current research, the simulation method is used to study the system. However, with the increasing number of sub-modules (SMs), it is difficult to model and simulate the system. In order to overcome these difficulties, this paper presents a universal mathematical model (UMM) of MMC using half-bridge cells as SMs. The UMM is a full-scale model with switching state, capacitance, inductance, and resistance characteristics. This method can calculate any number of SMs, and it does not need to build a simulation model (SIM) of physical MMC—in particular, parametric design can be realized. Compared with the SIM, the accuracy of the proposed UMM is verified, and the computational efficiency of the UMM is 8.7 times higher than the simulation method. Finally, by utilizing the proposed UMM method, the influence of the parameters of MMCs is studied, including the arm induction, SM capacitance, SM number, and output current/voltage total harmonic distortion (THD) based on the UMM in the paper. The results offer an engineering insight to optimize the design of MMCs.